Visibility in a ringworld atmosphere?

Question

So I am proposing a ring-world of approximately 1600 km diameter. The ring spins for earth like gravity. The ring itself would be several kilometers thick with Earth like variations in elevation (i.e. mountains less than ~8 km above sea level, with ocean trenches of similar depth) The atmosphere would also be the same composition as Earth's. The ring would have Earthlike lighting levels.

The question: How far could you see in any direction?

I would think there would be a limit to how far you could see before the atmosphere would haze and limit your sight distance when looking towards the horizon (although there wouldn't be a horizon; maybe along the ring is a better term), but looking upward further past a certain point the haze should fade and you would be able to see the farther sections of the ring. Is this correct?

Could someone help me out with specifics; distances, angles, etc? How would this change with elevation? Does less dense air equal farther sight distances?

Thanks!

Answer 1

I did some googling, and the best answer to how far the atmosphere of Earth would let you see if it went on forever was in this post in Reddit:

The dominant effect should be the diffraction limit of your eye. You can resolve two objects separated by an angle theta equal to wavelength of light / diameter of telescope. For your eye, theta ~ 500 nm / 0.5 cm = 10^-4 radians. If you had a building H meters tall at a distance of D, then you could see tan(theta) ~ theta ~ H/D (the first part comes from the small angle approximation), or H = 10^-4 * D. So, at 10 km (10⁴ m), you could resolve a 1 meter object. At 10,000 km, you could resolve a 1 km structure. By "resolve", in this case, it would be your ability to see the object against the surface of the ground.

Ten thousand kilometers is larger than your ring world by around an order of magnitude, so while haze would affect visibility just as it does on Earth, you would be able to see quite well in all directions.

Now, one thing to consider about your atmosphere. If it has the same composition and density as ours, and in a ringworld with the same average temperature and gravity as those from Earth, the stratosphere should be approximately 18-19 km deep. Let's round it to twenty. This calculator (in the "Area of circle segment by radius and height" part of the page) gives us a chord length of aroud 504.38 kilometers. That's the longest distance light can travel in your world without leaving the atmosphere. That's two orders of magnitude greater than the distance to the horizon on sea level on Earth. Your world, though smaller than Earth, would provide its inhabitants with quite a sight.

Edit: Just to make things clear (no pun intended), haze and refraction would have their maximum effect on objects around 500 kilometers away from the observer. Farther than that, haze and refraction are actually reduced. But you'll see the whole ring in all directions without much distortion.

Answer 2

There are a number of factors that would influence how things actually look from the inside surface of a ringworld:

1. The diameter of the ring affects how noticeable the curvature is at short distances, well before the following factors come into play. The diameter and width also affect the apparent magnitude of the opposite side of the ring, which determines whether it can be seen, e.g., during the day.

2. As suggested, atmospheric scattering results in a sky-blue haze when looking through long stretches of air, just as it does on Earth. In addition, clouds and/or dust can further obstruct one's view of the ring.

3. The atmosphere's decreasing pressure (and therefor decreasing index of refraction) at increasing altitudes also results in atmospheric refraction, again similarly to Earth. This causes light to bend back toward the ground; as a result, objects at intermediate distances appear more elevated with respect to the horizontal than they actually are.

4. Variations in air temperature and pressure also have an impact on the atmosphere's index of refraction. Extreme cases on Earth produce mirages such as Fata Morgana. Due to the upward curvature of the ring, these effects may be more pronounced at certain distances and light-lines passing through them may be more prone to yield reflected images of the ground (as opposed to the sky).

It is difficult to determine which of the above effects will dominate for a given viewing angle, but we can consider some specific cases. A thorough discussion of simulating atmospheric haze can be found on the FlightGear wiki, in which the authors suggest 500 km of visibility is possible on exceptionally clear days, though visibility can be greatly reduced due to atmospheric conditions. For a 1600 km diameter ring with 19 km of atmosphere, the longest (straight) chord remaining entirely within the atmosphere is about 350 km and pertains to a viewing angle of roughly 12.5° above the horizontal. Atmospheric refraction should bend that angle's corresponding light-line slightly toward the ring, in effect shortening the amount of air it actually passes through. Accordingly, and especially because much of the atmosphere said light-line traverses has greatly reduced density, we can judge that observers should be able to see the ring structure with at most partial haze between 0 and 12.5° in ideal weather conditions. On the other hand, if visibility is a mere 100 km, then the ring would become fully obscured by haze from about 3.6° until somewhere around 12.5°.

As for larger angles, light-lines pass through less total atmosphere, thereby resulting in less atmospheric scattering, but the apparent magnitude of the viewed portion of the ring structure is also reduced because it is further away. That being said, if we assume the 1600 km diameter ring to have approximately the same albedo as the moon and to have a width of around 15 km, then the far side of the ring would have the same angular width as the moon as viewed from Earth and, thus, would also have the same apparent magnitude. Similar to the light and dark portions of a crescent moon, illuminated sections of the ring would be plainly visible even in full daylight while dark sections would not be seen.

Increasing the viewer's altitude affects the above in that (a) it reduces the maximum viewing angle and length of light-lines staying entirely within the atmosphere and (b) such light-lines pass through air of overall lesser density. As a result, viewers at higher altitudes see less haze and the haze they do see occurs at angles either nearer to or below the horizontal.

As a last discussion topic, unlike atmospheric refraction, inferior mirages (e.g., due to layers of hot air very near the ground) cause light-lines to bend away from the ring. Because of the ring's upward curvature, this has the interesting potential to continue bending for far greater distances than is possible on Earth, meaning that unexpectedly distant objects may appear reflected (and quite likely stretched or squashed) in the mirage. Such mirages, however, usually require an extremely small viewing angle of less than 0.36° with respect to the horizontal, which is only possible for distances up to 10 km along the surface of a 1600 km diameter ring. On the other hand, superior mirages (e.g., due to temperature inversion) cause light-lines to bend even more toward the ring and may be especially prone to reflect objects of intermediate distance (say, 100 to 300 km for a similarly sized ring) such that they appear to float in the "sky" above more distant terrain. How frequently either of these phenomena occur depends on the kind of weather and terrain present on the ringworld; in particular, inferior mirages are most frequent in deserts while superior mirages are most frequent over oceans and frozen ground.